The Marlin Model 28 was Marlin's first hammerless, pump action shotgun. It was a 12 gauge gun made from 1913 to 1923. It was made in 4 different grades along with a Trap Grade and a Trap Special grade. The standard gun was the "A" grade, the next step up had checkered stocks with a Special Smokeless Steel barrel and was the "B" grade. The next step was an engraved gun with checkered fancy walnut stocks and a Special Smokeless Steel barrel. The best grade was the "D" grade gun with better engraving, fancier checking on Circiassian walnut stocks with either a Special Smokeless Steel barrel or a Damascus barrel. The Trap guns were special guns with made to order stocks, either a straight grip or pistol grip style.
The barrel serial number is interesting, but the "F" indicates it is a full choke barrel, probably either 30 or 32 inches in length.
If the 775 is the entire serial number on the receiver, then it may be a first year production gun. If there is a letter with the serial number, that changes the date to sometime after 1916.
Marlin has advised owners of any of the older pump action shotguns not to shoot them. I am not familiar with the hammerless guns, so I do not know the inner workings to tell you how to go about checking it to see if it is safe to shoot.
Value of any antique firearm is dictated by the amount and condition of the remaining original factory finish on the wood and metal. Without knowing these conditions, it is not possible to give an accurate estimation of value. Check some of the internet gun sites to see what a gun in similar condition to your gun has actually sold for to get an idea of value.

Due to the increasing cost of ammunition, there be no warning shot!

The growing federal deficit = generational slavery to the national debt.